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3 years ago

A motorboat takes 5 hours to travel 100 kilometers going upstream. The return trip takes

Mathematics

1 answer:

tatuchka [14]3 years ago

8 0

Step-by-step explanation:

Let's say b is the rate of the boat in still water, and c is the rate of the current.

Distance = rate × time

Going upstream:

100 = (b − c) (5)

20 = b − c

Going downstream:

100 = (b + c) (2)

50 = b + c

Solve the system of equations using substitution or elimination. Using elimination, add the equations together:

70 = 2b

b = 35

c = 15

The boat's speed is 35 km/h, and the current's speed is 15 km/h.

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Answer:

Step-by-step explanation:

(10 pushups)/(25 sec) = (⅖ pushup)/sec

Or,

(25 sec)/(10 pushups) = (2.5 sec)/pushup

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2 years ago

How do I graph (5, -3), (0, -4)

Lorico [155]

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Step-by-step explanation:

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2 years ago

What percent of 200 miles is 150 miles

Bumek [7]

150 / 200 = 0.75

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3 0

2 years ago

Read 2 more answers

What is one benefit of privately issued student loans?

Leona [35]

Answer:

they have lower interest rates and can be paid back with a lower out of pocket cost

Step-by-step explanation:

Student loans are issued as a kind of financial aid that assist students in their quest to acquire higher education. Private student loans are offered by the private-sector lenders. The alternative to this is a Federal loan.

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6 0

2 years ago

<img src="https://tex.z-dn.net/?f=Simplify%3A%20%5Cfrac%7B%205%C3%97%2825%29%5E%7Bn%2B1%7D%20-%2025%20%C3%97%20%285%29%5E%7B2n%7

Katen [24]

$\green{\large\underline{\sf{Solution-}}}$

<u>Given expression is </u>

$\rm :\longmapsto\:\dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} }$

can be rewritten as

$\rm \: = \: \dfrac{5 \times { {(5}^{2} )}^{n + 1} - {5}^{2} \times {5}^{2n} }{5 \times {5}^{2n + 3} - {( {5}^{2} )}^{n + 1} }$

We know,

$\purple{\rm :\longmapsto\:\boxed{\tt{ {( {x}^{m} )}^{n} \: = \: {x}^{mn}}}} \\$

And

$\purple{\rm :\longmapsto\:\boxed{\tt{ \: \: {x}^{m} \times {x}^{n} = {x}^{m + n} \: }}} \\$

So, using this identity, we

$\rm \: = \: \dfrac{5 \times {5}^{2n + 2} - {5}^{2n + 2} }{{5}^{2n + 3 + 1} - {5}^{2n + 2} }$

$\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 4} - {5}^{2n + 2} }$

can be further rewritten as

$\rm \: = \: \dfrac{{5}^{2n + 2 + 1} - {5}^{2n + 2} }{{5}^{2n + 2 + 2} - {5}^{2n + 2} }$

$\rm \: = \: \dfrac{ {5}^{2n + 2} (5 - 1)}{ {5}^{2n + 2} ( {5}^{2} - 1)}$

$\rm \: = \: \dfrac{4}{25 - 1}$

$\rm \: = \: \dfrac{4}{24}$

$\rm \: = \: \dfrac{1}{6}$

<u>Hence, </u>

$\rm :\longmapsto\:\boxed{\tt{ \dfrac{5 \times {25}^{n + 1} - 25 \times {5}^{2n} }{5 \times {5}^{2n + 3} - {25}^{n + 1} } = \frac{1}{6} }}$

4 0

2 years ago